On Statistical Properties of Jizba-Arimitsu Hybrid Entropy
arXiv:1611.02157 · doi:10.1016/j.physa.2017.02.009
Abstract
Jizba-Arimitsu entropy (also called hybrid entropy) combines axiomatics of Rényi and Tsallis entropy. It has many common properties with them, on the other hand, some aspects as e.g., MaxEnt distributions, are completely different from the former two entropies. In this paper, we demonstrate the statistical properties of hybrid entropy, including the definition of hybrid entropy for continuous distributions, its relation to discrete entropy and calculation of hybrid entropy for some well-known distributions. Additionally, definition of hybrid divergence and its connection to Fisher metric is also discussed. Interestingly, the main properties of continuous hybrid entropy and hybrid divergence are completely different from measures based on Rényi and Tsallis entropy. This motivates us to introduce average hybrid entropy, which can be understood as an average between Tsallis and Rényi entropy.
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